dig NS @1.1.1.1 test.herokuapp.com -> fail
dig @1.1.1.1 test.herokuapp.com -> fail
dig NS @dns1.p03.nsone.net test.herokuapp.com -> works
dig @dns1.p03.nsone.net test.herokuapp.com -> works
So my conclusion is that NS1 is having issue responding DNS queries from other DNS servers. Interestingly, there is no public information on heroku being dependent on NS1 or any current outages from NS1 status page.